Lattice QCD Plaquette Action as Discrete Ricci Curvature for Gauge Fields — E8 Intelligence Research

FINDING: Lattice QCD plaquette action is linked to discrete Ricci curvature, enabling non-perturbative geometric analysis of gauge fields. MATH: Plaquette action \( S_P = β ∑plaquettes (1 - 1/N Re Tr(U_P)) \), with \(β = 2N/g^2\) for SU(N). Discrete Ricci curvature defined via parallel transport around plaquettes, analogous to sectional curvature in Riemannian geometry. No explicit constants like 0.618 or 1.618 appear in the provided sources. CONNECTION: The lattice structure (hypercubic, 4D) is a discrete approximation to continuum spacetime, with plaquettes forming 2D faces. This connects to crystallographic symmetries (cubic lattice, root system \(A_3\) for SU(4) or \(D_4\) for SO(8) in 4D). No direct harmonic ratios (0.382, 0.618, etc.) are evidenced. DEPTH: 7 — The link between lattice gauge theory and discrete curvature is a profound step toward non-perturbative quantum gravity and geometry, but the provided sources lack explic Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com